抢渡长江最优路径的讨论

给出了2003年全国大学生数学建模竞赛D题的一种求解方法.运用拉格朗日乘数法与变分法建立了水速变化时最优路径适合的方程.特别针对问题4,当水流速度线性变化时,导出了求解最优解的函数方程.     

Lie algebroid morphisms, Poisson sigma models, and off-shell closed gauge symmetries

Chern–Simons (CS) gauge theories in three dimensions and the Poisson sigma model (PSM) in two dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as homotopies of such morphisms. We point out that the (off-shell) gauge symmetries of the PSM in the literature are not globally well defined for non-parallelizable Poisson manifolds and propose a covariant definition of the off-shell gauge symmetries as left action of some finite-dimensional Lie algebroid.

Our approach allows us to avoid complications arising in the infinite-dimensional super-geometry of the BV- and AKSZ-formalism. This preprint is a starting point in a series of papers meant to introduce Yang–Mills type gauge theories of Lie algebroids, which include the standard YM theory, gerbes, and the PSM.     

Coupling of cavity modes and guiding modes in two-dimensional phononic crystals

Cavity modes for the single-cavity and the double-cavities in two-dimensional phononic crystal are studied by using a plane waves expansion supercell method. We show that the single-cavity behaves like an atom while the double-cavities behave like a molecule. Couplings of cavity modes with the waveguide modes are investigated for typical configurations. Suitably designed waveguides with introduced cavities might be used as acoustic filter in waveguide applications.     

High temperature magnetic ordering in La2RuO5

Magnetic susceptibility, heat capacity and electrical resistivity measurements have been carried out on a new ruthenate, La₂RuO₅ (monoclinic, space group P2₁/c) which reveal that this compound is a magnetic semiconductor with a high magnetic ordering temperature of 170 K. The entropy associated with the magnetic transition is 8.3 J/mol K close to that expected for the low spin (S=1) state of Ru⁴⁺ ions. The low temperatures specific heat coefficient γ is found to be nearly zero consistent with the semiconducting nature of the compound. The magnetic ordering temperature of La₂RuO₅ is comparable to the highest known Curie temperature of another ruthenate, namely, metallic SrRuO₃, and in both these compounds the nominal charge state of Ru is 4+.     

High accuracy time and space transform method for advection–diffusion equation in an unbounded domain

A new numerical method called high accuracy time and space transform method (TSTM) is introduced to solve the advection–diffusion equation in an unbounded domain. By a spatial transform, the advection–diffusion equation in the unbounded domain Rⁿ is converted to one on the bounded domain [?1, 1]ⁿ, and the Laplace transform is applied to eliminate time dependency. The consequent boundary value problem is solved by collocation on Chebyshev points. To face the well‐known computational challenge represented by the numerical inversion of the Laplace transform, Talbot's method is applied, consisting of numerically integrating the Bromwich integral on a special contour by means of trapezoidal or midpoint rules. Numerical experiments illustrate that TSTM has exponential rate in time and space. Copyright © 2008 John Wiley & Sons, Ltd.     

Retrieving the complex degree of spatial coherence of electron beams

The possibility to characterize the coherence properties of an electron source is presented. The method, based on the determination of centered-reduced moments of the beam spot, allows the evaluation of both amplitude and phase of the complex degree of spatial coherence. The experimental results are in agreement with a different approach based on the Fourier analysis and with calculations according to the Van Cittert—Zernike theorem.     

A new sharpened version of the Neuberg–Pedoe inequality

In this work, we present a new sharpened version of the classical Neuberg–Pedoe inequality. As an application, the following improved Neuberg–Pedoe inequality is derived:

     

协差阵奇异时的最优投资组合

给出了协差阵半正定且有n-r个零特征值的一般情况下,Markowitz均值——方差最优投资组合模型的解及由单纯形表求得n-r个无风险基金权重的最优解.